Events
Department of Mathematics and Statistics
Texas Tech University
Regular sequences are a fundamental tool in commutative algebra. In
this talk, we introduce a notion of regular sequences in \(R\)-linear
triangulated categories, where \(R\) is a graded-commutative ring acting
centrally. As applications of this definition, we show that the length
of a regular sequence provides lower bounds on levels and on the
Rouquier dimension. This is joint work with Janina C. Letz and Marc
Stephan.
Join Zoom Meeting https://texastech.zoom.us/j/91729629174?pwd=TFJHbDk1ZS9KeTBRaldNL1hUbVNlQT09
Meeting ID: 937 0527 6265
Passcode: 508863
Abstract: This talk explores advanced numerical techniques, multigrid methods and acceleration strategies, for solving partial differential equations (PDEs) and nonsmooth optimization problems.
Part I: Advanced Multigrid Methods We begin by introducing multigrid methods alongside local Fourier analysis, a mathematical tool for predicting multigrid performance. Recent interest in poroelasticity has highlighted the challenges of finite-element discretizations and preconditioners, stemming from strong coupling, saddle-point structure, and wide parameter ranges. We present a solver-friendly discretization of the poroelastic Biot model using reduced quadrature, enabling efficient monolithic multigrid methods. Local Fourier analysis guides parameter tuning, and numerical results confirm the robustness and efficiency of the approach.
Part II: Acceleration Techniques for Fixed-Point Iteration The second part focuses on acceleration methods, particularly Anderson acceleration (AA) and nonlinear GMRES (NGMRES), which enhance the convergence of fixed-point iterations. We apply AA to accelerate the alternating least squares method for canonical tensor decomposition and analyze its convergence properties. We propose a generalized alternating Anderson acceleration scheme--a periodic hybrid of fixed-point and AA steps with tunable window sizes--offering flexibility for both linear and nonlinear problems. To demonstrate the applicability of our novel approach, we apply it to accelerate the alternating direction method of multipliers (ADMM) in solving nonlinear, nonsmooth optimization problems. We also investigate NGMRES($m$) applied to Richardson iteration for solving linear systems, establishing theoretical connections with classical Krylov subspace GMRES. We propose an alternating NGMRES, and provide convergence analysis of NGMRES applied to nonlinear systems.
When: 4:00 pm (Lubbock's local time is GMT -6)
Where: room Math 011 (Math Basement)
ZOOM details:
- Choice #1: use this link
Direct Link that embeds meeting and ID and passcode.
- Choice #2: join meeting using this link
Join Meeting, then you will have to input the ID and Passcode by hand:
* Meeting ID: 949 9288 2213
* Passcode: Applied
abstract 2 PM CST (UTC-6)
Zoom link available from Dr. Brent Lindquist upon request.